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Standard Deviation Formula Standard Deviation Formula Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" exists from the average (mean, or expected value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data points are spread out over a large range of values. The standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler though practically less robust than the average absolute deviation.[1][2] A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data. In addition to expressing the variability of a population, standard deviation is commonly used to measure confidence in statistical conclusions. Know More About How to Calculate Standard Deviation


For example:- The margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. The reported margin of error is typically about twice the standard deviation ­– the radius of a 95 percent confidence interval. In science, researchers commonly report the standard deviation of experimental data, and only effects that fall far outside the range of standard deviation are considered statistically significant – normal random error or variation in the measurements is in this way distinguished from causal variation. Standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment. When only a sample of data from a population is available, the population standard deviation can be estimated by a modified quantity called the sample standard deviation, explained below. Consider a population consisting of the following eight values:

2, 4, 4, 4, 5, 5, 7, 9 These eight data points have the mean (average) of 5: (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 5 Learn More About What is Standard Deviation


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Standard Deviation Formula